```-- | Some functions and generators suitable for writing QuickCheck
-- properties.

module Agda.Utils.TestHelpers
( -- * Algebraic properties
associative
, commutative
, idempotent
, isZero
, identity
, leftDistributive
, rightDistributive
, distributive
-- * Generators
, natural
, positive
, maybeGen
, maybeCoGen
, listOfElements
, elementsUnlessEmpty
, two
, three
-- * Test driver.
, runTests
)
where

import Data.Functor
import Test.QuickCheck

------------------------------------------------------------------------
-- Algebraic properties

-- | Is the operator associative?

associative :: (Arbitrary a, Eq a, Show a)
=> (a -> a -> a)
-> a -> a -> a -> Bool
associative (+) = \x y z ->
x + (y + z) == (x + y) + z

-- | Is the operator commutative?

commutative :: (Arbitrary a, Eq a, Show a)
=> (a -> a -> a)
-> a -> a -> Bool
commutative (+) = \x y ->
x + y == y + x

-- | Is the operator idempotent?

idempotent :: (Arbitrary a, Eq a, Show a)
=> (a -> a -> a)
-> a -> Bool
idempotent (/\) = \ x ->
(x /\ x) == x

-- | Is the element a zero for the operator?

isZero :: (Arbitrary a, Eq a, Show a)
=> a -> (a -> a -> a)
-> a -> Bool
isZero zer (*) = \x ->
(zer * x == zer)
&&
(x * zer == zer)

-- | Is the element a unit for the operator?

identity :: (Arbitrary a, Eq a, Show a)
=> a -> (a -> a -> a)
-> a -> Bool
identity one (*) = \x ->
(one * x == x)
&&
(x * one == x)

-- | Does the first operator distribute (from the left) over the
-- second one?

leftDistributive
:: (Arbitrary a, Eq a, Show a)
=> (a -> a -> a) -> (a -> a -> a)
-> a -> a -> a -> Bool
leftDistributive (*) (+) = \x y z ->
x * (y + z) == (x * y) + (x * z)

-- | Does the first operator distribute (from the right) over the
-- second one?

rightDistributive
:: (Arbitrary a, Eq a, Show a)
=> (a -> a -> a) -> (a -> a -> a)
-> a -> a -> a -> Bool
rightDistributive (*) (+) = \x y z ->
(x + y) * z == (x * z) + (y * z)

-- | Does the first operator distribute over the second one?

distributive
:: (Arbitrary a, Eq a, Show a)
=> (a -> a -> a) -> (a -> a -> a)
-> a -> a -> a -> Bool
distributive (*) (+) = \ x y z ->
leftDistributive (*) (+) x y z &&
rightDistributive (*) (+) x y z

------------------------------------------------------------------------
-- Generators

-- | Generates natural numbers.

natural :: (Integral i) => Gen i
natural = fromInteger . abs <\$> arbitrary

-- | Generates positive numbers.

positive :: (Integral i) => Gen i
positive = succ <\$> natural

-- | Generates a list of elements picked from a given list.
listOfElements :: [a] -> Gen [a]
listOfElements [] = return []
listOfElements xs = listOf \$ elements xs

-- | If the given list is non-empty, then an element from the list is
-- generated, and otherwise an arbitrary element is generated.

elementsUnlessEmpty :: Arbitrary a => [a] -> Gen a
elementsUnlessEmpty [] = arbitrary
elementsUnlessEmpty xs = elements xs

-- | Generates values of 'Maybe' type, using the given generator to
-- generate the contents of the 'Just' constructor.

maybeGen :: Gen a -> Gen (Maybe a)
maybeGen gen = frequency [ (1, return Nothing)
, (9, Just <\$> gen)
]

-- | 'Coarbitrary' \"generator\" for 'Maybe'.

maybeCoGen :: (a -> Gen b -> Gen b) -> (Maybe a -> Gen b -> Gen b)
maybeCoGen f Nothing  = variant 0
maybeCoGen f (Just x) = variant 1 . f x

-- | Generates two elements.

two :: Gen a -> Gen (a, a)
two gen = liftM2 (,) gen gen

-- | Generates three elements.

three :: Gen a -> Gen (a, a, a)
three gen = liftM3 (,,) gen gen gen

------------------------------------------------------------------------
-- Test driver

-- | Runs the tests, and returns 'True' if all tests were successful.

runTests :: String    -- ^ A label for the tests. Used for
--   informational purposes.
-> [IO Bool]
-> IO Bool
runTests name tests = do
putStrLn name
and <\$> sequence tests
```